We consider the problems of estimation and selection of parameters endowed
with a known group structure, when the groups are assumed to be sign-coherent,
that is, gathering either non-negative, non-positive or null parameters. To
tackle this problem we propose a new penalty that we call the cooperative-Lasso
penalty. We derive the optimality conditions defining the cooperative-Lasso
estimate for generalized linear models and propose an efficient active set
algorithm suited to high-dimensional problems.